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I have expanded the definition section a little, added mentioning of alternative definitions to the shear map being proper (“Bourbaki properness”), namely Palais’ definition in one of its many forms (“Palais properness”) highlighted the need of local compactness for these to be equivalent, added pointer to the original article by Palais, mentioned his attribution of the concept to Borel. Also pointer to Bourbaki, but didn’t actually look that up.
added the example that every smooth action of a compact Lie group on a smooth manifold is proper (here)
diff, v4, current
The reference is wrong, I do not find anything in Cor. 7.2 of Lee (either of the cited books), moreover the statement is obvious for any action of a compact topological group, without any smoothness…
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